NUMERICAL ANALYZING METHOD, ELEMENT ANALYZING BLOCKS, AND PROCESSING APPARATUS FOR NUMERICAL ANALYSIS

摘要

The present invention provides a numerical analyzingmethod, by which equations of every element of a phenomenonrepresented by partial differential equations can be solvedindependently from each other by the direct method or theiteration method without using any collocation method such asthe domain decomposition method, the finite difference methodor the finite element method.A defined domain is decomposed in mesh (S1); statevectors in each element of the mesh are approximated bypolynomials of finite number of terms with respect tocoordinate variables (S2); and then conditions betweendifferent undetermined coefficients satisfying given goveringequations are obtained. Next equations representingrelationships between the undetermined coefficients of eachelement (element state equations) required for satisfyingcontinuity conditions of state vectors on peripheralboundaries of every element are obtained by the least squaresmethod to obtain a square matrix equation (S4). Further anelement matrix at that time is reduced by decomposition (S5),taking the boundary conditions given on the periphery intoaccount, and square matrix equations thus obtained are solvedeither by the iteration method as it is, in case where theyare separated from each other, or by the direct method as awhole (S6). State vectors at arbitrary points are calculatedby using calculation results obtained in this way.